Asset Classes: Bond Prices and Yields
Kerry Back
BUSI 721, Fall 2022
JGSB, Rice University
Coupons vs Yields
The coupon rate of a bond is set at the time of its issue.
However, what one anticipates earning on a bond varies with the market price.
- Price < par \(\Rightarrow\) coupon + capital gain
- Price > par \(\Rightarrow\) coupon - capital loss
What one would earn per year on a bond if held to maturity (assuming no default) is called the bond yield.
A bond yield is calculated as the internal rate of return on the bond, if purchased at the market price and held to maturity, assuming no default.
Because it assumes no default, it is sometimes called the promised yield.
- Recall that the internal rate of return is the discount rate that makes the \(\text{NPV} = 0\).
- Because bonds usually pay semi-annual coupons, the convention in calculating yields is to use semi-annual compounding.
- So, we calculate a semi-annual rate \(\text{r}\) that makes \(\text{NPV}=0\) and the yield is y=2r.
- Higher price \(\Leftrightarrow\) Lower yield and vice versa.
Calculating Yields
- Consider a bond that pays coupon cc semi-annually and has face value of 100.
- Let \(n\) denote the number of coupon payments remaining and \(\text{P}\) the bond price.
- Suppose the next coupon payment is six months away.
The yield is \(\text{y}\) that satisfies
\[P=\frac{c}{1+y/2}+\frac{c}{(1+y/2)^2}+\cdots+\frac{c+100}{(1+y/2)^n}\]
8A
- Yields are market-determined interest rates.
- Interest rates vary over time.
- At a point in time, interest rates vary by maturity and by credit quality.
- Variation by maturity can be seen from Treasury yields.
- Variation by credit quality can be seen from corporate yields.
- Corporate and other bonds are rated:
1.AAA=best quality
2.AA
3.A
4.BBB=worst investment grade
5.BB=best non-investment grade
6.B
7.CCC
8.\(\ldots\)
8B
8C